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Stock-Based Compensation and Shareholders' Equity - Textual (Details) - USD ($)
$ / shares in Units, shares in Thousands, $ in Millions
3 Months Ended 6 Months Ended
Jan. 30, 2021
May 01, 2021
May 02, 2020
Oct. 31, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Total intrinsic value of options exercised   $ 61.0 $ 35.3  
Total unrecognized compensation cost related to unvested share-based awards, before tax consideration   $ 382.2    
Weighted-average period to recognize compensation cost   1 year 6 months    
Total grant-date fair value of vested stock options   $ 94.2 $ 113.4  
Stock-based compensation   $ 6.0   $ 5.8
Number of shares authorized to be repurchased (in shares)   158,000    
Stock repurchase program, authorized amount   $ 1,600.0    
Performance Stock Option        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Number of shares authorized (in shares) 460      
Exercise price per share (in dollars per share) $ 144.06      
Award vesting period 5 years      
Average closing price period 70 days      
Maxim | Performance-based Restricted Stock Units        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Award vesting period   2 years    
Units granted (in shares)   121    
Minimum | Performance Stock Option        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Target percentage 0.00%      
Minimum | Maxim | Performance-based Restricted Stock Units        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Target percentage   0.00%    
Maximum        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Stock repurchase program, authorized amount   $ 6,600.0    
Maximum | Performance Stock Option        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Target percentage 100.00%      
Maximum | Maxim | Performance-based Restricted Stock Units        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Target percentage   200.00%